Systems of Equations/Inequalities Module 4 Systems of Equations/Inequalities

4.01 – Solve by graphing – 14 points Answer: (x,y) where the two lines cross Different slopes Consistent & independent Answer: no solution Same slopes with a different y-intercept Inconsistent Answer: infinitely many Same slopes with the same y-intercept Consistent & dependent

Definitions Consistent – equations intersect Inconsistent – no solution Independent – finite (limited) number of solutions Dependent – infinite (no limit) number of solutions

How to solve by graphing Put each equation in slope intercept form (y=mx+b) Graph both equations on the same graph Determine the solution. If there is one, you must name it ‘(x,y)’ where they cross. If there is none, then the answer is ‘no solution.’ If there are infinitely many, then the answer is ‘infinitely many.’

Solving Linear Equations Using Graphing Video Example Solving Linear Equations Using Graphing

4.02 Solve by Substitution – 15 points

Example #1

Example #2

Word problems Use the words to write your own two equations Use the answers they give you when you need help Example:

Solving Linear Systems Using Substitution Video Example Solving Linear Systems Using Substitution

4.03 Solve by Elimination Addition Using

Addition Using

Multiplication Using

Multiplication Using

Solving Linear Systems Using Elimination Video Example Solving Linear Systems Using Elimination

4.04 System of Inequalities When you graph the equations using Desmos or by hand, chose the areas that are shaded by both equations If you aren’t sure about a point (if it is included in the solution, or the shaded part) you can test it by plugging it in to both equations (x & y) and see if the equation is true

Graphing Inequalities Before you graph systems of inequalities, you must know how to first graph one inequality.

Solving Systems of Inequalities Video Example Solving Systems of Inequalities

4.05 Linear Programming Use a graphing program or graph by hand to plug in the equations https://www.desmos.com/calculator You will have multiple lines and you will need to know what your vertices of the feasible region are The feasible region is the part of the graph that is shaded by all of the equations you have or where they intersect Vertices Feasible region

One purpose of linear programming is to find out how to maximize profit or minimize cost for a business Once you have graphed your system of inequalities and found the vertices, you will plug those values in to your objective function to find your max or min value

Linear Programming Basics Video Examples Linear Programming Basics Linear Programming Word Problem